Papers by Krerley Oliveira
Differential and Integral Equations
In this paper we study the existence, regularity and geometric properties of an optimal configura... more In this paper we study the existence, regularity and geometric properties of an optimal configuration to a free boundary optimization problem governed by the p-Laplacian.
PLOS ONE
By the peak of COVID-19 restrictions on April 8, 2020, up to 1.5 billion students across 188 coun... more By the peak of COVID-19 restrictions on April 8, 2020, up to 1.5 billion students across 188 countries were affected by the suspension of physical attendance in schools. Schools were among the first services to reopen as vaccination campaigns advanced. With the emergence of new variants and infection waves, the question now is to find safe protocols for the continuation of school activities. We need to understand how reliable these protocols are under different levels of vaccination coverage, as many countries have a meager fraction of their population vaccinated, including Uganda where the coverage is about 8%. We investigate the impact of face-to-face classes under different protocols and quantify the surplus number of infected individuals in a city. Using the infection transmission when schools were closed as a baseline, we assess the impact of physical school attendance in classrooms with poor air circulation. We find that (i) resuming school activities with people only wearing ...
2019 32nd SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI)
Customer behavior analysis is an essential issue for retailers, allowing for optimized store perf... more Customer behavior analysis is an essential issue for retailers, allowing for optimized store performance, enhanced customer experience, reduced operational costs, and consequently higher profitability. Nevertheless, not much attention has been given to computer vision approaches to automatically extract relevant information from images that could be of great value to retailers. In this paper, we present a low-cost deep learning approach to estimate the number of people in retail stores in real-time and to detect and visualize hot spots. For this purpose, only an inexpensive RGB camera, such as a surveillance camera, is required. To solve the people counting problem, we employ a supervised learning approach based on a Convolutional Neural Network (CNN) regression model. We also present a four channel image representation named RGBP image, composed of the conventional RGB image and an extra binary image P representing whether there is a visible person in each pixel of the image. To extract the latter information, we developed a foreground/background detection method that considers the peculiarities of people behavior in retail stores. The P image is also exploited to detect the hot spots of the store, which can later be visually analyzed. Several experiments were conducted to validate, evaluate and compare our approach using a dataset comprised of videos that were collected from a surveillance camera placed in a real shoe retail store. Results revealed that our approach is sufficiently robust to be used in real world situations and outperforms straightforward CNN approaches.
arXiv (Cornell University), Mar 31, 2004
We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions... more We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of the SRB measure varies continuously with the dynamics. We apply our result to a vast class of non-uniformly expanding maps of a compact manifold and prove the continuity of the entropy of the SRB measure. In particular, we show that the SRB entropy of Viana maps varies continuously with the map.
Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, 2022
Marine oil spills may have devastating consequences for the environment, the economy, and society... more Marine oil spills may have devastating consequences for the environment, the economy, and society. The 2019 oil spill crisis along the northeast Brazilian coast required immediate actions to control and mitigate the impacts of the pollution. In this paper, we propose an approach based on Deep Learning to efficiently inspect beaches and assist response teams using UAV imagery through an inexpensive visual system. Images collected by UAVs through an aerial survey are split and evaluated by a Convolutional Neural Network. The results are then integrated into heatmaps, which are exploited to perform geospatial visual analysis. Experiments were carried out to validate and evaluate the classifiers, achieving an accuracy of up to 93.6% and an F1 score of 78.6% for the top trained models. We also describe a case study to demonstrate that our approach can be used in real-world situations.
Multimedia Tools and Applications, 2020
Measuring and analyzing the flow of customers in retail stores is essential for a retailer to bet... more Measuring and analyzing the flow of customers in retail stores is essential for a retailer to better comprehend customers' behavior and support decision-making. Nevertheless, not much attention has been given to the development of novel technologies for automatic people counting. We introduce LRCN-RetailNet: a recurrent neural network architecture capable of learning a non-linear regression model and accurately predicting the people count from videos captured by low-cost surveillance cameras. The input video format follows the recently proposed RGBP image format, which is comprised of color and people (foreground) information. Our architecture is capable of considering two relevant aspects: spatial features extracted through convolutional layers from the RGBP images; and the temporal coherence of the problem, which is exploited by recurrent layers. We show that, through a supervised learning approach, the trained models are capable of predicting the people count with high accuracy. Additionally, we present and demonstrate that a straightforward modification of the methodology is effective to exclude salespeople from the people count. Comprehensive experiments were conducted to validate, evaluate and compare the proposed architecture. Results corroborated that LRCN-RetailNet remarkably outperforms both the previous RetailNet
arXiv: Dynamical Systems, 2020
In the context of non-uniformly expanding maps, possibly with the presence of a critical set, we ... more In the context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. The technique consists in using an inducing scheme in a finite Markov structure with infinitely many symbols to code the dynamics to obtain an equilibrium state for the associated symbolic dynamics and then projecting it to obtain an equilibrium state for the original map.
Dynamical Systems, 2021
We examine uniqueness of equilibrium states for the natural extension of a topologically exact, n... more We examine uniqueness of equilibrium states for the natural extension of a topologically exact, non-uniformly expanding, local homeomorphism with a Hölder continuous potential function. We do this by applying general techniques developed by Climenhaga and Thompson, and show there is a natural condition on decompositions that guarantees that a unique equilibrium state exists. We then show how to apply these results to partially hyperbolic attractors.
Nonlinearity, 2020
We prove that a class of partially hyperbolic attractors introduced by Castro and Nascimento have... more We prove that a class of partially hyperbolic attractors introduced by Castro and Nascimento have unique equilibrium states for natural classes of potentials. We also show if the attractors are C 2 and have invariant stable and centerunstable foliations, then there is a unique equilibrium state for the geometric potential and its 1-parameter family. We do this by applying general techniques developed by Climenhaga and Thompson.
Journal of Statistical Physics, 2018
We define the notion of sequential Gibbs measures, inspired by on the classical notion of Gibbs m... more We define the notion of sequential Gibbs measures, inspired by on the classical notion of Gibbs measures and recent examples from the study of non-uniform hyperbolic dynamics. Extending previous results of Kempton-Pollicott [7] and Ugalde-Chazottes [2], we show that the images of one block factor maps of a sequential Gibbs measure are also a sequential Gibbs measure, with the same sequence of Gibbs times. We obtain some estimates on the regularity of the potential of the image measure at almost every point.
Stochastics and Dynamics, 2016
We prove the existence of relative maximal entropy measures for certain random dynamical systems ... more We prove the existence of relative maximal entropy measures for certain random dynamical systems of the type [Formula: see text], where [Formula: see text] is an invertibe map preserving an ergodic measure [Formula: see text] and [Formula: see text] is a local diffeomorphism of a compact Riemannian manifold exhibiting some non-uniform expansion. As a consequence of our proofs, we obtain an integral formula for the relative topological entropy as the integral of the logarithm of the topological degree of [Formula: see text] with respect to [Formula: see text]. When [Formula: see text] is topologically exact and the supremum of the topological degree of [Formula: see text] is finite, the maximizing measure is unique and positive on open sets.
Foundations of Ergodic Theory
EQUADIFF 2003 - Proceedings of the International Conference on Differential Equations, 2005
Transactions of the American Mathematical Society, 2013
In this paper we deal with an invariant ergodic hyperbolic measure μ for a diffeomorphism f, assu... more In this paper we deal with an invariant ergodic hyperbolic measure μ for a diffeomorphism f, assuming that f is either C 1+α or C 1 and the Oseledec splitting of μ is dominated. We show that this system (f, μ) satisfies a weaker and non-uniform version of specification, related with notions studied in several recent papers. Our main results have several consequences: as corollaries, we are able to improve the results about quantitative Poincaré recurrence, removing the assumption of the non-uniform specification property in the main theorem of "Recurrence and Lyapunov exponents" by Saussol, Troubetzkoy and Vaienti that establishes an inequality between Lyapunov exponents and local recurrence properties. Another consequence is the fact that any such measure is the weak limit of averages of Dirac measures at periodic points, as in a paper by Sigmund. One can show that the topological pressure can be calculated by considering the convenient weighted sums on periodic points whenever the dynamic is positive expansive and every measure with pressure close to the topological pressure is hyperbolic.
Proceedings of the American Mathematical Society, 2012
Exploring abundance and nonlacunarity of hyperbolic times for endomorphisms preserving an ergodic... more Exploring abundance and nonlacunarity of hyperbolic times for endomorphisms preserving an ergodic probability with positive Lyapunov exponents, we obtain that there are periodic points of period growing sublinearly with respect to the length of almost every dynamical ball. In particular, we conclude that any ergodic measure with positive Lyapunov exponents satisfies the nonuniform specification property. As consequences, we (re)obtain estimates on the recurrence to a ball in terms of the Lyapunov exponents, and we prove that any expanding measure is the limit of Dirac measures on periodic points.
Nonlinearity, 2006
We prove that, under a mild condition on the hyperbolicity of its periodic points, a map g which ... more We prove that, under a mild condition on the hyperbolicity of its periodic points, a map g which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map). In particular, this result gives a partial positive answer for a question done by A. Katok, in a related context.
Nonlinearity, 2004
We show that, for a robust (C 2-open) class of random nonuniformly expanding maps, there exists e... more We show that, for a robust (C 2-open) class of random nonuniformly expanding maps, there exists equilibrium states for a large class of potentials.In particular, these sytems have measures of maximal entropy. These results also give a partial answer to a question posed by Liu-Zhao. The proof of the main result uses an extension of techniques in recent works by Alves-Araújo, Alves-Bonatti-Viana and Oliveira.
Journal of the Institute of Mathematics of Jussieu, 2005
Given a compact n-dimensional immersed Riemannian manifold M n in some Euclidean space we prove t... more Given a compact n-dimensional immersed Riemannian manifold M n in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then M n is homeomorphic to the sphere S n. Also, we define a concept of finite geometrical type and prove that finite geometrical type hypersurfaces with small set of points of zero Gauss-Kronecker curvature are topologically the sphere minus a finite number of points. A characterization of the 2n-catenoid is obtained.
Journal of Statistical Physics, 2006
We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions... more We consider classes of dynamical systems admitting Markov induced maps. Under general assumptions, which in particular guarantee the existence of SRB measures, we prove that the entropy of the SRB measure varies continuously with the dynamics. We apply our result to a vast class of non-uniformly expanding maps of a compact manifold and prove the continuity of the entropy of the SRB measure. In particular, we show that the SRB entropy of Viana maps varies continuously with the map.
Journal of Statistical Physics, 2009
In this paper, we study non-uniformly expanding repellers constructed as the limit sets for a non... more In this paper, we study non-uniformly expanding repellers constructed as the limit sets for a non-uniformly expanding dynamical systems. We prove that given a Hölder continuous potential φ satisfying a summability condition, there exists non-lacunary Gibbs measure for φ, with positive Lyapunov exponents and infinitely many hyperbolic times almost everywhere. Moreover, this non-lacunary Gibbs measure is an equilibrium measure for φ.
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Papers by Krerley Oliveira